Whisk together the eggs, water, green onions, and salt and pepper in a large bowl. Heat the butter in a large nonstick saute pan over medium heat. Add the egg mixture and stir until soft curds form.
Place the toasted English muffins on a baking sheet and divide the sausage patties among the halves. Scatter about 1/4 cup of the cheese over top and place under the broiler for a minute or so, just until cheese is melted. Divide eggs over top of melted cheese, then ladle some of the gravy over, and garnish with green onion tops. Serve immediately, 2 halves per person.
Sausage and Gravy:
Form sausage into 4 patties and cook in a large skillet over medium-high heat until golden brown. Remove to a plate with a slotted spoon. Add the onion and jalapeno to the pan and cook until soft. Stir in the flour and cook for 1 1/2 to 2 minutes. Slowly whisk in the milk and bring to a boil, whisking constantly, until thickened. Lower the heat and cook for 5 minutes. Season with the sage and salt and pepper, to taste, and cook for 5 minutes longer.